English

On an exotic topology of the integers

General Topology 2010-08-05 v1 Number Theory

Abstract

We study some interesting properties of Furstenberg's topology of the integers. We show that it is metrizable, totally disconnected, and (Z,+,.) is a topological ring with respect to this topology. As an application, we show that any two disjoint sets of primes can be separated by arithmetic progressions.

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Cite

@article{arxiv.1008.0713,
  title  = {On an exotic topology of the integers},
  author = {Rezsö L. Lovas and István Mezö},
  journal= {arXiv preprint arXiv:1008.0713},
  year   = {2010}
}

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6 pages